Prime Factorization - Is Integer a Factor - From Value as Factors (Level 3)

This math topic focuses on advanced factoring and the determination of whether one integer is a factor of another using prime factorization. Involving skills like breaking numbers down to their prime factors and observing these factors' compatibility, students address questions that ascertain if a given number is a factor of another, based on their prime factor representations. This includes assessing compatibility and powers of prime constituents of the integers in question.

Is Integer a Factor - From Value as Factors

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Is 150 a factor of 2310

150=zmb22310=235711is 150 a factor of2310?\begin{align*}150 &= z \cdot m \cdot b^2\\\\[-0.5em]2310 &= 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11\end{align*}\\\\ \textsf{is }150\textsf{ a factor of}\\2310?